gerber



Jan. 31, 1956 A. GERBER 2,733,405

E. CIRCUIT FOR MEASURING THE PARAMETERS OF PIEZOELECTRIC CRYSTALS SWEEPFREQUENCY GENERATOR v INVENTOR.

EDUARD A, GERBER rl ffor zey E. A. GERBER Jan. 31, 1956 CIRCUIT FORMEASURING THE PARAMETERS OF PIEZOELECTRIC CRYSTALS Filed NOV. 27, 1951 2Sheets-Sheet 2 EDUARD A. GERBER 772 a W mej antiresonant circuit.

United States Patent CIRCUIT FOR SURING THE PARAMETERS OF PIEZOELECTRICCRYSTALS Eduard A. Gerber, Elberon, N.

States of America as represented by the Secretary of the ArmyApplication November 2 7 1951, Serial No. 258,498 6 Claims. (Cl. 324-56)(Granted under Title 35, U. s. Code 1952 sec. 266) J., assignor to theUnited be described by its equivalent circially at very highfrequencies, the frequency spectrum of a crystal is rather complicated.Besides the main resonant frequency response, it shows a multitude ofother resonance frequencies or spurious responses which may berepresented by similar networks, more .or less coupled together, as wellas the network representing the main response. a

The most important task in producing crystals for eflicient operation atvery high frequencies is to eliminate or at least reduce the spuriousresponses. To be ableto For a better understanding of the invention,together with other and further objects thereof, reference is had to thefollowing description taken in connection with the accompanying drawingin which:

Figure 1 discloses the equivalent electrical network of a piezoelectriccrystal; 1

Figure 2 is a circuit showing all the essential electrical circuitfeatures of the invention;

Figures 3, 4 and 5 are explanatory curves; and

Figures 6 and 7 illustrate graphs for determining correction functions.

Referring now to Figure l of the drawings, there. is shown a network 1which represents the equivalent electrical network of a piezoelectriccrystal which corresponds to the main resonance frequency of thecrystal. 'This is a conventional representation of the equivalentelectrical parameters of a crystal which is well known in the art andrequires no lengthy discussions. It should be noted that the networkcomprises a shunt capacitance Co connected in parallel with a seriescircuit comprising an inductance LS, resistance R5 and capacitance Cs. qt j The circuit shown in Figure 2 shows the elementary principle of theinvention and provides means for calculating or measuring the seriesresistance Rs and the series capacitance Cs of a crystal. At 10 there isshown an ultra-high frequency generator 'which is capable of providing afrequency sweep through a range of kilocycles in a period ofapproximately seconds. For example, if the frequency output of generator10 is originally'set for 30 megacycles, the frequency may be variedbetween 30 and 30.02 megacycles in a period of approximately 30 sec- 1ends. It is to be understood of course that other suitable perform thistask, measuring equipment is necessary which not only gives a survey ofthe crystal spectrum, but allows measurements to be taken of .theequivalent parameters of the main and spurious responses at the sametime. s

' It is the object of this invention therefore to provide a circuitmeans for quickly and accurately measuring the equivalent parameters.

It is a further object of this invention to provide an for determiningthe series resistance Rs, and the series crystal.

A still further object of the'invention is to measure the seriesresistance, R3 and the series capacitance. Cs of the main and spuriousresponses of a piezoelectric crystal by analyzing the frequencyspectrum.

In accordance with the present invention there is provided a highfrequency sweep generator, the output of which is applied to anantiresonant arrangement comprising an amplifier having the crystal tobe tested in the capacitance Cs, of a piezoelectric plate-cathodecircuit thereof, rectifier means for rectifying the antiresonantresponses, a filter network, and means for recording and measuring therectifiedantiresonant voltages corresponding to both the maiaandspurious responses of the crystal. The series resistance of the crystal,R5, is obtained by comparing the crystal antiresonant voltage peak withthe voltage recorded across a pure capacitive load which is alsoconnected in the the two antiresonantvoltages' giv'es'a measure fOfCs.

slow sweep rates may be employed. The output of generator 10 is appliedto input grid 12 of amplifier tube 14 ,by means of coupling capacitor 16and grid resistor 18 which is connected between grid 12 and ground.Cathode 11 of tube 14 is connected to ground through cathode resistor13. Cathode by-pass capacitor 15 is connected across resistor 13. Plate20 of tube 14 is connected to B+ through plate load resistor 22.Connected in parallel arrangement between plate 20 and ground are thecrystal 24, a variable capacitor 28 which may be connected to the platecircuit by switch 30 and the inherent plate circuit capacitance of thetube as represented by capacitor 26. The input voltage to grid 12 fromgenerator 10 may be designated as eg and the plate voltage developedacross the parallel tokeep the latter as small as possible so as tominimize- V the Miller effect'when measuring 8g. As hereinafterexplained, the plate voltage 'e is rectified and applied to a recorderunit 34. v

In order to accurately measure the relative amplitudes of 2;;corresponding to the main and spurious responses of crystal 24, there isprovided a rectifier circuit 36, a filter circuit 38, a residual currentcompensating circuit 40, and a conventional attenuator network 42. Asshown, the radio-frequency voltage e is coupledthrough capacitor 32 torectifier circuit 36 which includes the parallel arrangement of resistor44 and diode 46 connected between capacitor 32 and diode 46 is connectedto capacitor 32 andcathodeSWof diode 46 is grounded. t t g The output ofrectifier circuit "36 is applied to attenuator network 42 through seriesconnected filter resistors 52 and 54. Connected between the junction ofsaid resistors and ground is filter capacitor 56. Series connectedresistor 58 and potentiometer 60 are connected between the input ofattenuator network 42 and ground. Contact arm 61 of said potentiometeris grounded as ground. Plate 48 of to recorder unit as throughdirect-current amplifier 6S.

When the measuring. range is changed, any residual cu rent remaining indiode 46 is. compensated by diode 62 so that there is no variation inthe direct-current, or zero level, of therecorder unit. Filter network38' isolates crystal 24. from amplifier stage 68 in order to minimizethe influence ofthe input capacity thereof on the crystal. 7 Indetermining the series resistance Rs of the crystal it is to be assumedthat the plate-cathode resistanceot tub-e 14 and the reactance of theinherent capacitance 26 are both larger than the crystal resistance Rsat the main resonant frequency of the crystal, is usuallythe case. Theantiresonant impedance of the. crystal is then approximately equal tothe, performance index whichrmay be expressed by the following equation:

w CX 1Ba Where w=resonant frequency of crystal multipled by 21rC1=includes all the capacitance of the plate circuit and the staticcapacity C 7 Rs=series resistance of the crystal The method forobtaining the series resistance Rs consists in comparing theantiresonant voltage e i at a predetermined output frequency from signalgenerator 10 with that'of a second plate voltage e z developed across apure capacitive load. The predetermined frequency may correspond to themain frequency response or any of the spurious frequency responses to betested. It is to be assumed that switch 30 is open so that variablecapacitor 28 is not included in the plate circuit for this case.

As shown in Figure 3, e may represent the'antiresonant voltage developedacross the crystal at a frequency f1. It is to be understood that e imay correspondto either the main frequency response or any of, thespurious responses. e z represents the voltage developed across a pure,capacitive load. Because the reactance of a predetermined capacitor maybe too low, plate voltage e z may,

be developed by merely removing crystal 24 from. its 7 socket, thusutilizing the inher ent capacitance of the tube,

as represented by capacitor 26, as the pure capacitive load.

With the crystal removed from its socket, theindication \of cm mayremain constant within a narrow range of frequencies as shown in Figure3. i

It can beshown that i where It is well known, that to obtain a purecapacitive load, the plate circuit resistance of tube 14, which includesplate load resistor 22, the dynamic plate resistance of said tubeand'the inputresistance to diode 46,- must be very much greater than thereactance of the inherent plate circuit capacitance C2 of the tube 14.Thus, at very high frequencies R1 may be so large as compared to thevalue of PI that R1 need not be calculated. Assuming this to be thecase, it can be seen that by substituting the value of PI, as determinedin Equation 1, in Equation 2, crystal resistance R5 may be readilydetermined.

If the value of R1 is such that it cannot be neglected, then its valuemay be determined by the following method: Crystal 24 is removed fromthe plate circuit of tube 14 and variable capacitor 28 is switched intothe plate circuit of tube 14 by switch 30. Crystal 24 is respectivelyreplaced by at least three discrete inductances. Each of the threeinductances is individually connected in parallel with variablecapacitor 28 thus replacing the crystal unit which, as mentioned above,has been removed from the plate circuit of said amplifier tube. Each ofthe inductances selected is such that, for one given frequency, at leastthree different readings on the dial of capacitor 28 corresponding toresonance may be obtained. Thus, each of the three inductances areseparately and individually connected in parallel with variablecapacitor 28 and three distinct readings of capacitor 28 are obtainedfor each inductance. The quality factor Q of each coil may readily bedetermined in the conventional manner by means of a bridge or a Q meterat the predetermined frequency where w=operating frequency multiplied by21r gm;transc'onductance of the amplifier tube e =input voltage to theamplifier tube at operating fre- 'quency Cr=capacitance which resonateswith the coil at freqnency Qr=quality; factor of inductance atfrequency- R1=resistance of the plate circuit By plotting QLfordifierent values of I it C1. 1 I 7 Q against (g mand 8g are constantvalues and neednot be known) as shown n.Figu re.4, the value of R1 maybe easily determined. As shown,

R1 is the intercept of line L with the abscissa v QL Of course, thismeasurement may be made at different frequencies to obtain values of R1over the operating frequency range for which the crystal may be tested.Thus R1 may be determined within any given frequency range so that if itis desired to utilize this range of frequencies, the correspondingvalues of R1 may readily be obtained. (This determination of R1 has tobe done only once.) Summing up, it may be stated that at very highfrequencies, the value of R1 need not be determined but at relative lowfrequencies the value of R1 may be determined from Equation 3 andsubstituted in Equation 2 to calculate Rs- Series capacitance Cs may bedetermined as follows:

Crystal 24 is replaced in the plate circuit of amplifier tube 14 andvariable capacitor 28 is removed from the plate circuit by openingswitch 30. The output of frequency generator is swept from high to lowfrequency. For example, if the crystal is designed to operate at 30 mc.,then the output frequency generator 10 may be swept from 30.01 me. to29.99 me. It is desirable to measure the series capacitance Cs for aparticular mode of operation such as is shown in Figure 5. When theoutput of generator 10 passes the antiresonant peak of the mode selectedas indicated on recorder unit 34, capacitor 28, having a predeterminedcapacitive value, is again switched into the plate circuit by closingswitch 30 so that it is now in parallel arrangement with crystal 24. Atthis moment the antiresonant frequency of crystal 24 isdecreased to f4because of the added parallel capacitance. Thus, as the sweep frequencydecreases from the previous antiresonant frequency f3, a newantiresonant frequency f4 is approached and recorded. These first andsecond antiresonant voltages are shown in Figure 5 and are designated as6133 and e r respectively. The frequency difference between saidantiresonant peaks is desig nated by For actually determining Af, it isnecessary to have a frequency calibration of the recorder. As is wellknown this may be accomplished by amplitude modulating signal generator10 with a known audio frequency. The distance between one sideband andthe main response furnishes a frequency mark which may be used forcalibrating recorder unit 34. This frequency difference is a measure ofthe value of capacitance Cs in accordance with the following expression:

where Aw=Frequency difference X211- w=1St resonant frequency 21rC1=original capacitance in parallel with crystal AC1=capacitance addedin parallel with crystal.

Since all the factors on the right side of Equation 4 are known, Cs mayreadily be determined.

It is to be understood that for the validity of Equations 2 and 4, thesame restrictions are in force as for Equation 1, namely, that if R1 anddoes not hold true, more complicated expressions must replace Equations2 and 4.

In order to make the above methods applicable to high frequencies whereis small, correction functions may be derived in accordance with theconformal representation method shown by C. W. Harrison in Bell SystemsTechnical Journal, volume 24, pp. 217-252, April 1945. The followingexpressions derived by means of conformal representation may besubstituted respectively for Equations 2 and 4 where where X1 and X. arecorrection functions.

Since 1+X1 i 03 0 13, R1 is the absolute peak value of the totalimpedance'Z'r, as measured, the value of Rs may be determined from thefollowing expression:

R1 may be included in the correction function X1, to give anothercorrection function. X and the following expression may be written forEquation 7:

X1, X2 and X3 may be represented as functions of the followingrelations:

In Figures 6 and 7, X1 and X2 are plotted as a function of K fordifferent values of A. In Figure 7, the curves are also plotted forthree different values of Looking at Figure 6 it can be seen that theerror in measuring R5 is approximately 10% for a value of K as large as/0.1. That means for instance that, in case a me. crystal with C1 of 154 1f. if R5 is expected to be larger than 35 ohms.

While there have been described what at present are considered to be thepreferred embodiment of the invention, it will be understood by thoseskilled in the art that various changes and modifications may be madeherein without departing from the invention, and it is, therefore, aimedin the appended claim to cover all such modifications and changes asfall within the spirit and scope of the invention.

What is claimed is:

1. The method of determining the series resistance of a socket mountedpiezoelectric crystal comprising, the steps of generating a voltage at apredetermined frequency corresponding to the main or spurious frequencymode of operation of said crystal, amplifying said generator voltage,applying said amplified generator voltage across said crystal inparallel arrangement with the amplifier output to develop anantiresonant voltage across the crystal at said predetermined frequency,rectifying and recording said antiresonant voltage, removing saidcrystal from its socket, rectifying and recording the voltage developedin the output circuit of said amplifier with the crystal removed fromits socket, and deriving the series resistance of said crystal from saidrectified and recorded. voltages.

2. The method of determining the series resistance of a piezo-electriccrystal comprising the steps of generating a voltage at a predeterminedfrequency corresponding to the main or spurious frequency mode ofoperation of said crystal, amplifying said generator voltage, applyingsaid amplified generator voltage across said crystal in parallelarrangement with the amplifier output to develop an antiresonant voltageacross the crystal at said predetermined frequency, rectifying andrecording said antiresonant voltage, applying said amplifier generatedvoltage across a pure capacitive load, rectifying and record ing thevoltage generated across said pure capacitive load, and deriving theseries resistance of said crystal from said rectified and recordedvoltages.

3. 'The method of determining the series capacitance of a piezo-electriccrystal comprising the stcps of generating a voltage through a range offrequencies corresponding to the main and spurious modes of frequencyoperation of said crystal, amplifying said generator voltage, applyingsaid amplified voltage across said crystal in parallel arrangement withthe amplifier o t .it to develop apeak voltage across said crystal at arust antiresonant frequency, rectifying andrecording said firstantiresonant frequency voltage, connecting a capacitive reactance inparallel arrangement with said crystal when the frequency L output ofsaid generator passes the peak of said first antiresonant voltage,applying said generator voltage across the-parallel combination of saidcrystal and said capacitive rectance to develop a voltage across saidcrystal at a second antiresonant frequency, rectifying and recording thesecond antiresonant frequency voltage, and deriving the seriescapacitance of said crystal from the difference in frequency of saidfirst and' second antiresonant frequencies.

4. A method of determining the series resistance of a socket-mountedpiezoelectric crystal comprising the steps of generating a voltage at apredetermined frequency corresponding to the main or suprious frequencymode of operation of said crystal, applying said generator voltageacross said crystal in parallel arrangement with the generator output todevelop an anti-resonant voltage across said crystal at saidpredetermined frequency, recording the magnitude of said anti-resonantvoltage, removing the crystal from the generator output circuit,substituting for said crystal a pure capacitive load applying saidgenerator voltage across said pure capacitive load, recording themagnitude of the voltage developed across saidpure capacitive load, andderiving the series resistance of said crystal from said recordedvoltages.

5. A method of determining the series capacitance of a piezoelectriccrystal comprising the steps of generating a voltage through a range offrequencies corresponding to the main and spurious modes of frequencyoperation of saidcrystal, amplifying said generator voltage, applyingsaid. amplifiedvoltage across said crystal in. parallel arrangernentwith the, output of; the amplifier, to develop a voltage. across thecrystal at a first, anti-resonant fre-. quency, recordingsaidanti-resonant frequency, connecting. a. capacitive reactance-inparallel arrangementwith saidcrystal when the frequency output of saidgenerator passes the anti resonant peak of said first anti-resonantvoltage, applying said generator voltage across the parallel combinationof: said crystal and said capacitive reactance to develop a voltage at asecond anti-resonant frequency, recording said second anti-resonantfrequency and deriving the. series capacitance of said crystal from thedifference in frequency of said first and second anti-resonantfrequencies.

6. The method of determining the series capacitance of a piezoelectriccrystal comprising the steps of generating a voltage through a range offrequencies corresponding to the main and spurious modes of frequencyoperation of said crystal, applying said generated voltage across afirst parallel arrangement of' the crystal and a first predeterminedcapacitive reactance to develop a peak voltage across said crystal at afirst antiresonant frequency, recti fying and recording saidfirstantiresonant frequency voltage, connecting a second capacitivereactance across said first parallel arrangementto form a secondparallel arrangement at the instant the voltage output of said gen-.erator reaches said peak voltage, applying said generator voltage acrossthe second parallel arrangement to develop a peak voltage at a secondantiresonant frequency, rectifying and recording said secondantiresonant frequency voltage, and deriving the series capacitance inaccordance with the formula T AC,

where Aw=difierence in frequency between said first and sec- 0ndantiresonant frequencies 21r w=fiISt antiresonant frequencyx 21rC1=capacitance in first parallel arrangement AC1=capacitance added tothe first parallel arrangement.

7 References Cited in the file of this patent UNITED STATES PATENTS

